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GRIP: scalable 3D global routing using integer programming
 In IEEE Design Automation Conf
, 2009
"... We propose GRIP, a scalable global routing technique via Integer Programming (IP). GRIP optimizes wirelength and via cost without going through a layer assignment phase. GRIP selects the route for each net from a set of candidate routes that are generated based on an estimate of congestion generated ..."
Abstract

Cited by 8 (3 self)
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We propose GRIP, a scalable global routing technique via Integer Programming (IP). GRIP optimizes wirelength and via cost without going through a layer assignment phase. GRIP selects the route for each net from a set of candidate routes that are generated based on an estimate of congestion generated by a linear programming pricing phase. To achieve scalability, the original IP is decomposed into smaller ones corresponding to balanced rectangular subregions on the chip. We introduce the concept of a floating terminal for a net, which allows flexibility to route long nets going through multiple subregions. We also use the IP to plan the routing of long nets, detouring them from congested subregions. For ISPD 2007 benchmarks, we obtain 3.9 % and 11.3 % average improvement in wirelength and via cost for the 2D and 3D versions respectively, compared to the best results reported in the open literature.
Efficient preprocessing for vlsi optimization problems. submitted to
 Comp. Opt. Theory and Appl
, 2006
"... Advances in technology for the manufacturing of integrated circuits have resulted in extremely large, and time consuming, problems on how to lay out components for optimal circuit performance. Although these problems can be written as a linear program, due to the very high number of variables invol ..."
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Cited by 2 (1 self)
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Advances in technology for the manufacturing of integrated circuits have resulted in extremely large, and time consuming, problems on how to lay out components for optimal circuit performance. Although these problems can be written as a linear program, due to the very high number of variables involved in solving these problems, it is of upmost importance to preprocess these problems both efficiently and well before attempting their solution. Fortunately, VLSI problems have a remarkably well structured constraint matrix, which allows for some novel preprocessing techniques. In this report we examine efficient preprocessing for the linear programs resulting from VLSI circuit design. We provide analysis showing our preprocessing techniques are accurate and more efficient than traditional preprocessing techniques, as well as provide some numerical testing demonstrating the increased efficiency.
Algorithms, Theory, and Computational Practice
, 2008
"... Global routing in VLSI (very large scale integration) design is one of the most challenging discrete optimization problems in computational theory and practice. In this paper, we present a polynomial time algorithm for the global routing problem based on integer programming formulation with a theore ..."
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Global routing in VLSI (very large scale integration) design is one of the most challenging discrete optimization problems in computational theory and practice. In this paper, we present a polynomial time algorithm for the global routing problem based on integer programming formulation with a theoretical approximation bound. The algorithm ensures that all routing demands are satisfied concurrently, and the overall cost is approximately minimized. We provide both a serial and parallel implementation as well as develop several heuristics used to improve the quality of the solution and reduce running time. We provide computational results on a two sets of wellknown benchmarks and show that, with a certain set of heuristics, our new algorithms perform extremely well compared with other integerprogramming models. 1
Global Routing in VLSI Design: Algorithms, Theory, and Computational Practice
"... Global routing in VLSI (very large scale integration) design is one of the most challenging discrete optimization problems in computational theory and practice. In this paper, we present a polynomial time algorithm for the global routing problem based on an integer programming formulation. The algor ..."
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Global routing in VLSI (very large scale integration) design is one of the most challenging discrete optimization problems in computational theory and practice. In this paper, we present a polynomial time algorithm for the global routing problem based on an integer programming formulation. The algorithm features a theoretical approximation bound while ensuring all the routing demands are concurrently satisfied. We provide both a serial and a parallel implementation as well as develop several heuristics to improve the quality of the solution and reduce running time. Our computational results on a wellknown benchmark set show that, combined with certain heuristics, our new algorithms perform extremely well compared with other integer programming approaches. 1
Title: Improving solution times in VLSI optimization problems Authors:
, 2006
"... The problem of wire layout (or routing) in VLSI design can be written as a large scale linear program with upper bound constraints. Due to the size of these programs, optimization by use of classical methods can be extremely time consuming. This report surveys some of the recent techniques and ideas ..."
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The problem of wire layout (or routing) in VLSI design can be written as a large scale linear program with upper bound constraints. Due to the size of these programs, optimization by use of classical methods can be extremely time consuming. This report surveys some of the recent techniques and ideas which have been emerging on how to improve the time required to solve these highly structured linear programs. Techniques for improving the runtime for these linear programs generally fall into two categories: improving existing software and creating new algorithms. The first method is generally done by applying novel preprocessing techniques before using preexisting software or by parameter tuning on the software. The second approach is generally accomplished by exploiting the specific structure of the linear programs created in VLSI design. In this report we begin by discussing two preprocessing techniques which have shown some promise in VLSI design. We follow this with a discussion on parameter tuning in CPlex version 10. The parameter tuning strongly suggests that the best way to solve these linear programs is to embed the upper bound constraints into the constraint matrix and then solve via interior point methods. This naturally leads to the question of how to best embed the upper bound constraint into the constraint matrix. We explore several new methods to do this, and discuss how each of these methods affects the work required to calculate the Newton directions associated with interior point methods. 1
IEEE TRANSACTIONS ON COMPUTERAIDED DESIGN OF INTEGRATED CIRCUITS AND SYSTEMS, VOL., NO. 1 GRIP: Global Routing via Integer Programming
"... Abstract—This work introduces GRIP, a global routing technique via integer programming. GRIP optimizes wirelength and via cost directly without going through a traditional layer assignment phase. Candidate routes spanning all the metal layers are generated using a linear programming pricing phase th ..."
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Abstract—This work introduces GRIP, a global routing technique via integer programming. GRIP optimizes wirelength and via cost directly without going through a traditional layer assignment phase. Candidate routes spanning all the metal layers are generated using a linear programming pricing phase that formally accounts for the impact of existing candidate routes when generating new ones. To make an integerprogrammingbased approach applicable for today’s largescale global routing instances, the original problem is decomposed into smaller subproblems corresponding to rectangular subregions on the chip together with their net assignments. Route fragments of nets that fall in adjacent subproblems are connected in a flexible manner. In case of overflow, GRIP applies a secondphase optimization that explicitly minimizes overflow. By using integer programming in an effective manner, GRIP obtains highquality solutions. Specifically, for the ISPD 2007 and 2008 benchmarks, GRIP obtains an average improvement in wirelength and via cost of 9.23 % and 5.24%, respectively, when compared to the best result in the open literature. Index Terms—Global Routing, Integer Programming.
Global Routing in VLSI Design: Algorithms, Theory, and Computational Practice
"... Global routing in VLSI (very large scale integration) design is one of the most challenging discrete optimization problems in computational theory and practice. In this paper, we present a polynomial time algorithm for the global routing problem based on integer programming formulation with a theore ..."
Abstract
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Global routing in VLSI (very large scale integration) design is one of the most challenging discrete optimization problems in computational theory and practice. In this paper, we present a polynomial time algorithm for the global routing problem based on integer programming formulation with a theoretical approximation bound. The algorithm ensures that all routing demands are satisfied concurrently, and the overall cost is approximately minimized. We provide both serial and parallel implementation as well as develop several heuristics used to improve the quality of the solution and reduce running time. We provide computational results on two sets of wellknown benchmarks and show that, with a certain set of heuristics, our new algorithms perform extremely well compared with other integerprogramming models. Key words: Global routing in VLSI design, Approximation algorithms, Integer programming model. ∗ Corresponding author.